A = l x w

π = 3.14

 

7th Grade

Math Facts

 

 

4 + 6 = 6 + 4

 

½ = 0.5

 

 

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Types of Numbers

 

1.        Natural Numbers (Counting Numbers) are the set of numbers that begin with 1, 2, 3, 4, etc.

2.        Whole numbers are the set of numbers that begin with 0, 1, 2, 3, 4, etc.

3.        A whole number that has more than two factors is a composite number.

4.        A prime number has exactly two factors, 1 and the number itself.

5.        Writing a composite number as a product of primes is called prime factorization.

6.        Integers are positive and negative whole numbers, including zero.

7.        Positive numbers and negative numbers are opposites.

8.        The sum of two opposites is always zero.

9.        Subtracting two integers can be done by adding it’s opposite.

10.     When multiplying /dividing two numbers with the same sign, the product / quotient will always be positive.

11.     When multiplying / dividing two numbers with different signs, the product / quotient will always be negative.

12.     A rational number is a number that can be written as a fraction, where the denominator cannot be zero.

13.     A number that is represented by a non-repeating, non-terminating decimal is called an irrational number.

14.     When solving a problem with multiple operations, use the order of operations PEMDAS: Parenthesis, Exponents, Multiplication or Division (left to right), Addition or Subtraction (left to right)

15.     The absolute value of a number is the distance between the number and zero on a number line.

 

Fractions, Decimals and Percents

 

16.     A fraction is a quotient of two numbers where the denominator is not zero.

17.     The number on the top of a fraction is called the numerator.

18.     The number on the bottom of a fraction is called the denominator.

19.     A fraction where the numerator is greater than the denominator is called an improper fraction.

20.     A mixed number has a whole number and a fraction.

21.     Two fractions that are equal to each other are called equivalent fractions.

22.     To add or subtract two fractions you need to have a common denominator.

23.     The least common denominator (LCD) of two fractions can be found by finding the lowest common multiple of the two denominators.

24.     Simplifying fractions is dividing the numerator and the denominator by their greatest common factor (GCF)

25.     The greatest common factor (GCF) of two numbers is the greatest number that is a factor of both numbers.

26.     When multiplying two fractions, multiply the two numerators together and the two denominators together.

27.     To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.

28.     Two numbers are reciprocals if their product is one.

29.     To convert a fraction to a decimal, take the numerator divided by the denominator.

30.     A repeating decimal is a decimal in which a digit or a sequence of digits keeps repeating.

31.     A terminating decimal is a decimal that stops, or terminates.

32.     A percent (%) is a ratio that compares a number to 100.

33.     To convert a decimal to a percent, multiply the decimal by 100, or move the decimal point 2 places to the right.

34.     Decimals, percents and fractions are different ways to write the same number.

 

Ratios and Proportions

 

35.     A proportion is an equation stating that two ratios are equal.

36.     A ratio is a comparison of two numbers by division.

37.     To solve proportions, cross multiply and divide.

 

Exponents

 

38.     A base is the number or the variable that is being raised to a power.

39.     An exponent tells you how many times a base is used as a factor.

40.     A power is a number expressed using an exponent.

41.     Scientific Notation is a way of writing very large numbers and very small numbers using powers of ten.

42.     A perfect square is the product of two identical numbers.  4² = 4 x 4 = 16

43.     The square root of a number is a number which when multiplied by itself equals the given number.

44.     A radical √ is the symbol used to denote a square root.

45.     Any number raised to the zero power equals one.   4º = 1

Expressions and Equations

 

46.     An expression is a mathematical sentence that contains numbers and / or variables, separated by operation signs.

47.     An equation is a mathematical sentence showing that two expressions are equal to each other.

48.     Any value or values that make an equation true is called a solution.

49.     Inverse operations are operations that undo each other (addition « subtraction; multiplication « division; square « square root)

50.     A symbol, usually a letter, which stands for a number, is called a variable.

 

Inequalities

 

51.      An inequality is a comparison of two expressions.

52.      < is the symbol for less than.

53.      > is the symbol for greater than.

54.      ≤ is the symbol for less than or equal to

55.      ≥ is the symbol for greater than or equal to.

56.      ≠ is the symbol for not equal to.

 

Properties

 

57.     The associative property of addition and multiplication says that if numbers are grouped together differently, the expressions will still remain equal.  ( 1 + 2 ) + 3 = 1 + ( 2 + 3 ) and 4 · ( 5 · 6 ) = ( 4 · 5 ) · 6

58.     The commutative property of addition and multiplication says that when you change the order, the expressions will still remain equal.   7 + 8 = 8 + 7 and 9 · 10 = 10 · 9

59.     The distributive property shows that a · ( b + c ) = a·b + a·c.  You multiply “a” by each “b” and by “c”.                          2 ( 3 + 4 ) = 2 · 3 + 2 · 4

60.     The zero property of multiplication states that the product of zero and any number is zero.  5 · 0 = 0

 

Data and Statistics

 

61.     Data is information gathered.

62.     Frequency is the number of times something occurs in a set of data.

63.     The mean (average) of a set of data is the sum of the data divided by the number of items in the set of data.

64.     The median is the middle number when the data is in numerical order.

65.     The mode of a set of data is the data item that occurs most often.

66.     The range of a set of numerical data is the difference between the greatest and least values of the set.

67.     A data item that is far apart from the rest of the data is an outlier.

68.     A histogram is a bar graph that represents frequency of data.

69.     Line graphs represent how data changes over time.

70.     Circle graphs are best for comparing parts to a whole

 

Probability

 

71.     Probability is used to describe how likely it is that an event will happen.  It is the ratio of favorable outcomes to possible outcomes.

72.     To figure the probability of an event occurring: P(event) = Number of successful ways for an event to happen

Total number of possible outcomes

73.     An outcome is a possible result.

74.     Theoretical probability is what “should” happen.

75.     Experimental probability is what “does” happen.

76.     When two events have no effect on each other they are considered independent events.

77.     When a second event is affected by the result of a previous event, it is called dependent events.

 

 

Points, Lines and Angles

 

78.     A mathematical tool that is used to measure an angle is called a protractor.

79.     An angle is made up of two rays that share a common endpoint called the vertex.

80.     An angle that measures exactly 90 degrees is called a right angle.

81.     An angle that measures greater than 90 degrees, but less than 180 degrees is called an obtuse angle.

82.     An angle that measures less than 90 degrees is called an acute angle.

83.     Two angles that are side by side and share a common ray are called adjacent angles.

84.     Two adjacent angles, whose measurements add up to 90 degrees, are called complementary angles.

85.     Corresponding angles are created when a transversal intersects two parallel lines.

86.     Vertical angles are congruent angles formed whenever two lines intersect.

87.     An angle that measures exactly 180 degrees is called a straight angle.

88.     Two adjacent angles, whose measurements add up to 180 degrees are, called supplementary angles.

89.     A straight path that extends in both directions forever is called a line.

90.     Lines that are in the same plane that will never intersect are called parallel lines.

91.     Perpendicular lines are lines that intersect to form right angles.

92.     A straight path that extends in one direction forever is called a ray.

93.     A line that intersects two parallel lines is called a transversal.

94.     An intersection is where two lines cross.

95.     The common endpoint where two rays intersect is called the vertex.

96.     A segment is part of a line.

97.     The midpoint of a segment is the point that divides the segment into two congruent segments.

 

Circles and Polygons

 

98.     A circle is a closed curve where all the points are the same distance from the center.

99.     Half of a circle is called a semicircle.

100.   An arc is part of a circle.

101.   A segment that passes through the center of a circle and has both endpoints on the circle is called the diameter.

102.   A segment that has one endpoint at the center of a circle and the other endpoint on the circle is called a radius.

103.   A segment that has both endpoints on the circle is called a chord.

104.   A closed plane figure formed by three or more line segments that do not cross is called a polygon.

105.   A regular polygon has all sides congruent and all angles congruent.

106.   A triangle is a polygon with three sides.

107.   An equilateral triangle has all equal sides and equal angles.

108.   An isosceles triangle has two equal sides and two equal angles.

109.   A scalene triangle has no equal sides and no equal angles.

110.   The sum of the angles in a triangle will always equal 180 degrees.

111.   Right triangles have one 90-degree angle.

112.   Obtuse triangles have one angle more than 90 degrees.

113.   Acute triangles have only acute angles.

114.   A quadrilateral is a polygon with four sides.

115.   A parallelogram is a quadrilateral that has two sets of parallel lines.

116.   A rectangle is a quadrilateral that has two sets of parallel lines and four right angles.

117.   A rhombus (diamond) is a quadrilateral that has four congruent sides and no right angles.

118.   A square is a quadrilateral with two sets of parallel lines, four right angles and four congruent sides.

119.   A trapezoid is a quadrilateral that has exactly one pair of parallel sides.

120.   The sum of the angles in a quadrilateral will always equal 360 degrees.

121.   A five-sided polygon is called a pentagon.

122.   A hexagon is a polygon with six sides.

123.   An eight-sided polygon is called an octagon.

124.   A decagon is a polygon with ten sides.

125.   If two figures are congruent, then they have the same measurement.

126.   Similar shapes have the same shape and angles, but not necessarily the same size.

 

 

 

 

 

Formulas

 

127.   Pi (π) is the ratio of the circumference to the diameter of a circle.  π = 3.14

128.   The number of square units needed to cover the inside of a figure is called the area.

129.   The area of a rectangle is A = l · w

130.   The area of a triangle is A = ½ · b · h

131.   The area of a square is A = s²

132.   The area of a parallelogram is A = b · h

133.   The area of a circle is A = π · r²

134.   The area of a trapezoid is A = ½ · h · ( b1 + b   )

135.   Perimeter is the distance around a figure.

136.   To find the perimeter of a polygon, add all sides together.

137.   The distance around a circle is called the circumference.

138.   The circumference of a circle if the radius is known is C = 2 · π  ·  r

139.   The circumference of a circle if the diameter is known is C = π  ·  d

140.   The surface area of a prism is the sum of the areas of the faces.

141.   The volume of a three-dimensional figure is the number of cubic units needed to fill the space inside the figure.

142.   The volume of a prism is V = l · w · h

143.   The volume of a cylinder is V = π · r² · h

144.   The Pythagorean Theorem states that in any right triangle, the sum of the squares of the lengths of the legs is  equal to the square of the length of the hypotenuse. ( a² + b²  = c² )

145.   The distance something travels is equal to the rate it travels multiplied by the time it takes to get there.   Distance = Rate · Time (D = R · T)

146.   Interest is the fee that a person pays when they borrow money from a bank.                                                 Interest = Principle · Rate · Time  ( I = P · R · T)

 

Coordinate planes

 

147.   A horizontal number line (x-axis) and a vertical number line (y-axis) form a coordinate plane.

148.   An ordered pair is a pair of numbers that describe the location of a point on a coordinate plane.

149.   The point of intersection of the x-axis and the y-axis on a coordinate plane is called the origin.

150.  The x-axis and y-axis divide the coordinate plane into four regions, called quadrants.                                         Quadrant I (+x, +y); Quadrant II (-x, +y); Quadrant III (-x, - y); Quadrant IV (+x, -y).

151.   A linear equation is an equation that forms a line.

152.   Slope is a ratio that describes the steepness of a line.

153.   A graph that has a positive slope has a line that goes from Quadrant III to Quadrant I.

154.   A graph that has a negative slope has a line that goes from Quadrant II to Quadrant IV.

155.   A graph with no slope is a vertical line.

156.   A graph with zero slope is a horizontal line.

157.   A function is a pairing of two sets of numbers where for every number in the first set there is only one corresponding number in the second set.

158.   The domain of a function is the x values.

159.   The range of a function is the y values.

 

Miscellaneous

 

160.   The answer to an addition problem is called the sum.

161.   The answer to a subtraction problem is called the difference.

162.   The answer to a multiplication problem is called the product.

163.   The answer to a division problem is called the quotient.

164.   A Venn diagram is a diagram that illustrates the relationships between objects or numbers.